The size of the Democratic advantage in the fight for control of the House is unclear with a month until the midterm elections, and there are recent signs Republicans might have improved their position, possibly because of the fight over Brett Kavanaugh’s nomination to the Supreme Court.

A favorable national environment, strong Democratic candidates and a wave of Republican retirements have combined to produce a long list of vulnerable Republican seats. But Republicans remain competitive in the districts that will decide control.

The sheer number of highly competitive districts means a wide range of possible outcomes. Democrats could win in a landslide, or Republicans could run the table and narrowly retain a majority. Both possibilities are evident in data collected from The New York Times Upshot/Siena College surveys in battleground districts.

If we assume for illustrative purposes that the Times/Siena surveys are basically right (we have polled or are currently polling 40-some races), Democrats have a comfortable advantage in enough Republican-held districts to give them 17 of the 23 seats they need to take a majority. (This assumes they’re also comfortably ahead in the “lean or likely” Democratic districts that we haven’t surveyed.)

To take the House, Democrats would then need to win only six out of the 17 Republican-held districts where the Times/Siena poll results have been within five points. And that doesn’t include the two dozen tossup or “lean Republican” districts where we haven’t conducted a poll.

With so many opportunities to win just a few more seats, it’s easy to see why the Democrats are considered favorites. And with so many opportunities over all, it’s easy to imagine how the Democrats could gain 40 or more seats. Even modest late movement toward the Democrats would topple many additional Republicans and potentially put an entire additional tier of seats into play.

On the other hand, modest late movement toward the Republicans could give the party a chance to sweep a pretty long list of tossup districts. Any number of factors could push the race one way or another.

The Kavanaugh factor

High-quality national, Senate and House polls have generally trended toward Republicans since the Kavanaugh hearing before the Senate Judiciary Committee.

Polls from Quinnipiac, Emerson, IBD, Reuters/Ipsos, YouGov and Marist showed the Democratic edge on the generic ballot falling by an average of four points. Monmouth polls in Virginia’s 10th District and Pennsylvania’s First showed the Democrats falling by three points. And five Fox News polls of top Senate races showed the Democratic edge falling by an average of two points.

Republicans posted some of their best Times/Siena polling results in weeks. Republicans led, sometimes comfortably, in tossup districts where Republican presidential nominees prevailed in both 2012 and 2016, like Virginia’s Second District, Michigan’s Eighth, North Carolina’s Ninth and Ohio’s First.

There were a few good polls for the Democrats as well, including Upshot/Siena polls in Arizona’s Second District, Michigan’s 11th and Minnesota’s Second. But the balance of evidence is consistent with the notion that the Republicans have made slight gains.

Curiously, the polls also show that Judge Kavanaugh’s support has steadily eroded over the last few weeks, including a precipitous decline since the hearing, beginning immediately the night of Sept. 27.

It might seem strange for Republicans to improve their standing even as Mr. Kavanaugh’s falls. It is even stranger since the Times/Siena polls provide zero evidence — truly, zero — to support the view that Republicans are now likelier to say they intend to vote than they were before the Kavanaugh hearing.

One possibility is that Republican enthusiasm is causing Republican-leaning voters to respond to telephone surveys, which might move the polls without moving the underlying race. Another possibility is that Judge Kavanaugh, despite his diminished standing, might represent a relatively good issue for Republicans, even if he’s not particularly popular in his own right. After all, he remains more popular than the president and Republicans on the generic ballot, which asks people whether they intend to vote for a Democrat or a Republican for Congress.

It’s also possible that the Kavanaugh controversy is helping Republicans in Republican-leaning areas. It’s consistent with the available evidence, but this could also be noise considering the small number of polls since the hearing.

A highly polarized electorate hurts Democrats
The possibility that the Kavanaugh nomination is helping Republicans in Republican-leaning areas is important because the fight for control of both the House and the Senate will be determined largely in Republican-leaning areas. This simple fact has always been the G.O.P.’s biggest advantage. If the electorate is polarized along the lines of recent presidential elections, as it was during the Obama presidency, Republicans could hold down their losses considerably.

Democrats have been considered clear favorites in the fight for House control because polls and special election results have made it seem that the electorate wouldn’t be so polarized, allowing them to compete in many Republican-leaning districts. But if Democrats can’t break through and actually carry the many Republican-leaning districts they’ve put into play, Republicans could stay highly competitive in the fight for House control and even survive a wave election.

Today’s House map is so favorable to Republicans that based on recent presidential election results, even a 2006- or 2010-type wave — even a rerun of the highly polarized Virginia governor’s and state legislative races last November — would yield only around a net-27 seats for Democrats, by our estimates. Yes, that would be enough for a majority, but it would be close enough that it wouldn’t take too much luck for Republicans to hold on.

The 2006 election is a particularly telling example. Democrats picked up 31 seats, not much more than Democrats need now, with a set of opportunities fairly similar to what the Democrats have today. And the Democratic gain was padded by many victories against Republicans embroiled in scandal. Without those gains, the Democrats might not have picked up the number of seats that Democrats need this year.

There’s another reason 2006 is a troubling example for Democrats: The Republicans avoided a total rout by winning around 20 districts by less than four points. It’s not hard to imagine something like that happening again. In fact, Republicans have led in 12 Upshot/Siena polls by less than four points already.

For now, Democrats aren’t yet favored to win in most of the Republican-held seats they’ve put into play. The FiveThirtyEight election forecast, which gives the Democrats around a 75 percent chance to win the House with an average pickup of 34 seats, makes the Democrats outright favorites only in 218 districts — precisely the number needed for a majority. The Democrats are favored to win so many more races than they currently lead because there’s a lopsided number of Republican-tilting districts where the Democrats are highly competitive.

At the moment, not much separates a Democratic landslide from a seat-by-seat, piecemeal battle for control that lasts late on election night — or for days longer as mail ballots are counted in California and Washington.